Structural Analysis of Nonbinary Cyclic and Quasi-Cyclic LDPC Codes with α-Multiplied Parity-Check Matrices

Abstract

In this letter, the structural analysis of nonbinary cyclic and quasi-cyclic (QC) low-density parity-check (LDPC) codes with α-multiplied parity-check matrices (PCMs) is concerned. Using analytical methods, several structural parameters of nonbinary cyclic and QC LDPC codes with α-multiplied PCMs are determined. In particular, some classes of nonbinary LDPC codes constructed from finite fields and finite geometries are shown to have good minimum and stopping distances properties, which may explain to some extent their wonderful decoding performances.